Asymptotics for Toeplitz determinants: perturbation of symbols with a gap
Mathematical Physics
2015-06-22 v2 Classical Analysis and ODEs
Complex Variables
math.MP
Abstract
We study the determinants of Toeplitz matrices as the size of the matrices tends to infinity, in the particular case where the symbol has two jump discontinuities and tends to zero on an arc of the unit circle at a sufficiently fast rate. We generalize an asymptotic expansion by Widom [22], which was known for symbols supported on an arc. We highlight applications of our results in the Circular Unitary Ensemble and in the study of Fredholm determinants associated to the sine kernel.
Keywords
Cite
@article{arxiv.1409.0435,
title = {Asymptotics for Toeplitz determinants: perturbation of symbols with a gap},
author = {Christophe Charlier and Tom Claeys},
journal= {arXiv preprint arXiv:1409.0435},
year = {2015}
}
Comments
28 pages, 5 figures